Answer:
C. \(2\text{ Inches}^2\)
Step-by-step explanation:
We have been given that length of rectangle is \(\sqrt[5]{16}\) inches and width is \(2^{\frac{1}{5}}\) inches. We are asked to find the area of the given rectangle.
\(\text{Area of rectangle}=\text{Length}\times \text{Width}\)
Substitute given values:
\(\text{Area of rectangle}=\sqrt[5]{16}\text{ Inches}\times 2^{\frac{1}{5}}\text{ Inches}\)
Writing 16 as \(2^4\).
\(\text{Area of rectangle}=\sqrt[5]{2^4}\text{ Inches}\times 2^{\frac{1}{5}}\text{ Inches}\)
Using property \(\sqrt[n]{a^m}=a^\frac{m}{n}}\), we will get:
\(\text{Area of rectangle}=2^{\frac{4}{5}}\text{ Inches}\times 2^{\frac{1}{5}}\text{ Inches}\)
\(\text{Area of rectangle}=2^{\frac{4}{5}}\times 2^{\frac{1}{5}}\text{ Inches}^2\)
Using property \(a^m\times a^n=a^{m+n}\), we will get:
\(\text{Area of rectangle}=2^{\frac{4}{5}+\frac{1}{5}}\text{ Inches}^2\)
\(\text{Area of rectangle}=2^{\frac{4+1}{5}}\text{ Inches}^2\)
\(\text{Area of rectangle}=2^{\frac{5}{5}}\text{ Inches}^2\)
\(\text{Area of rectangle}=2^{1}\text{ Inches}^2\)
\(\text{Area of rectangle}=2\text{ Inches}^2\)
Therefore, the area of the given rectangle is 2 square inches and option C is the correct choices.
